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Nonlinear evolution of singular disturbances to a tanh3y mixing layer

Published online by Cambridge University Press:  17 February 2009

S. Saujani ,
J. Drozd  and
R. Mallier
S. Saujani
Affiliation:
Department of Applied Mathematics, University of Western Ontario, London ON N6A 5B7, Canada.
J. Drozd
Affiliation:
Department of Applied Mathematics, University of Western Ontario, London ON N6A 5B7, Canada.
R. Mallier
Affiliation:
Department of Applied Mathematics, University of Western Ontario, London ON N6A 5B7, Canada.
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Abstract

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We consider the nonlinear evolution of a disturbance to a mixing layer, with the base profile given by u0(y) = tanh3y rather than the more usual tanh y, so that the first two derivatives of u0 vanish at y = 0. This flow admits three neutral modes, each of which is singular at the critical layer. Using a non-equilibrium nonlinear critical layer analysis, equations governing the evolution of the disturbance are derived and discussed. We find that the disturbance cannot exist on a linear basis, but that nonlinear effects inside the critical layer do permit the disturbance to exist. We also present results of a direct numerical simulation of this flow and briefly discuss the connection between the theory and the simulation.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 3 , January 2002 , pp. 409 - 427
Copyright
Copyright © Australian Mathematical Society 2002

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